For what value of k does the quadratic equation
kx(x – 2) + 6 = 0 have equal roots? (CBSE 2013)

Question

For what value of k does the quadratic equation(k +4) x2 + (k +1) x +1 = 0 have equal roots? (CBSE 2013)

Philoid · Accepted Answer

Let D be the discriminant of the given equation.

We have a = k + 4, b = k + 1, c = 1

D = b² – 4ac

= (k +1)² – 4(K + 4)(k + 1)

= k² + 1 + 2k – 4(k² + k + 4k + 4)

= = k² + 1 + 2k – 4k² - 4k - 16k – 16
= k² – 2k – 15

= k² – 5K + 3K – 15

= k(k – 5) + 3(k – 5)

= (k – 5) ( k + 3)

If roots are real, then

D = 0

⇒ (k – 5)(k + 3) = 0

⇒ k = 5,-3

For what value of k does the quadratic equation
(k +4) x² + (k +1) x +1 = 0 have equal roots? (CBSE 2013)